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Which value is similar to sin^-1sin(6 π/7)?(a) sin^-1(π/7)(b) cos^-1(π/7)(c) sin^-1(2π/7)(d) coses^-1(π/7)The question was posed to me in unit test.This intriguing question comes from Inverse Trigonometry topic in section Inverse Trigonometric Functions of Mathematics – Class 12

Answer» CORRECT CHOICE is (a) SIN^-1(π/7)

The best EXPLANATION: sin^-1sin(6 π/7)

Now, sin(6 π/7) = sin(π – 6 π/7)

= sin(2π + 6 π/7) = sin(π/7)

= sin(3π – 6 π/7) = sin(20π/7)

= sin(-π – 6 π/7) = sin(-15π/7)

= sin(-2π + 6 π/7) = sin(-8π/7)

= sin(-3π – 6 π/7) = sin(-27π/7)

THEREFORE, sin^-1sin(6 π/7) = sin^-1(π/7).


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